Breathers in inhomogeneous nonlinear lattices : an analysis via centre manifold reduction

We consider an infinite chain of particles linearly coupled to their nearest neighbours and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous, i.e. coupling constants, particle masses and on-site potentials can have small variations along the chain. We look for small amplitude and time-periodic solutions, and in particular spatially localized ones (discrete breathers). The problem is reformulated as a nonautonomous recurrence in a space of time-periodic functions, where the dynamics is considered along the discrete spatial coordinate. Generalizing to nonautonomous maps a centre manifold theorem previously obtained for infinite-dimensional autonomous maps [Jam03], we show that small amplitude oscillations are determined by finite-dimensional nonautonomous mappings, whose dimension ∗Corresponding author